HSG-GPE.B.4

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- HSG-GPE.B.4Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
- HSG-GPE.B.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
- HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

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HSG-GPE.B.7

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- HSG-GPE.B.4Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
- HSG-GPE.B.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
- HSG-GPE.B.6Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- HSG-GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

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## HSG-GPE.B.7

## Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

10 Lesson(s)

### Tools of Geometry Unit Assessment

Geometry »
Unit: Tools of Geometry

Geometry »
Unit: Tools of Geometry

Big Idea:

#### Test time! Students take the first unit assessment, aligned to the Common Core standards for this unit.

Standards:

Favorites
(8)

Resources
(13)

### Finding the Distance or the Midpoint of a Line Segment on the Coordinate Plane

Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents

Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents

Big Idea:

#### This lesson gains student interest using a Carnival Map and dives deeper using the Math Practices One, Two, and Four.

Standards:

Favorites
(16)

Resources
(9)

### Coordinate Geometry Unit Review and Test

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Big Idea:

#### Test time! Students review and then take the unit assessment, hopefully demonstrating their knowledge of coordinate geometry, as well as their ability to organize and justify their work.

Standards:

Favorites
(5)

Resources
(14)

### More Practice with Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Geometry »
Unit: Coordinate Geometry

Big Idea:

#### Students put their coordinate geometry knowledge to work, investigating characteristics of geometric figures and proving hypotheses.

Standards:

Favorites
(5)

Resources
(9)

Big Idea:

#### This is a comprehensive assessment of all content learned to date.

Standards:

Favorites
(1)

Resources
(12)

Reflections
(1)

### Distance in Geometry

Geometry »
Unit: The Pythagorean Theorem

Geometry »
Unit: The Pythagorean Theorem

Big Idea:

#### Understanding why the distance formula works with respect to the "change in x or y," enables students to solve novel problems requiring the measurement of distance.

Standards:

Favorites
(3)

Resources
(14)

Reflections
(1)

### Finding Perimeter and Area in the Coordinate Plane

Geometry »
Unit: Geometry Foundations

Geometry »
Unit: Geometry Foundations

Big Idea:

#### It's Gridlock. Trapped inside the coordinate plane, armed only with coordinate pairs and formulas, students must find perimeters and areas of triangles and rectangles.

Standards:

Favorites
(3)

Resources
(9)

Reflections
(1)

### Distances in the Coordinate Plane

Geometry »
Unit: Geometry Foundations

Geometry »
Unit: Geometry Foundations

Big Idea:

#### May the formula be with you. In this lesson students wield the power of the distance formula.

Standards:

Favorites
(35)

Resources
(15)

Reflections
(1)

### End of Year Assessment Review Day 3 of 4

Geometry »
Unit: Final Assessment

Geometry »
Unit: Final Assessment

Big Idea:

#### In this lesson, students practice problems involving concepts from the units on similarity, trigonometry and coordinate geometry.

Resources
(11)

Reflections
(1)

### Proving Area Formulas for Parallelograms, Triangles and Rhombuses

Geometry »
Unit: Areas of Plane Figures

Geometry »
Unit: Areas of Plane Figures

Big Idea:

#### Look deep within...and see a figure whose area formula we've already proven.

Standards:

Resources
(21)

Reflections
(1)

Common Core Math

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### Eighth Grade

### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School